Strongly disordered spin ladders

Mélin, R.; Lin, Yueh-hsiang; Lajkó, Péter; Rieger, Heiko; Iglói, Ferenc

doi:10.1103/physrevb.65.104415

Cited by 56 publications

(74 citation statements)

References 55 publications

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“…Melin et al 22 used the RSRG method as well as the density-matrix RG method to study the distribution of the energy gap separating the ground and first excited states in clusters ͑with lengths up to 512͒ of AF two-leg spin-1/2 ladders. They found that the dynamic exponent z that characterizes this distribution is nonuniversal and depends continuously on the randomness strength.…”

Section: Summary and Discussionmentioning

confidence: 99%

Thermodynamics of strongly disordered spin ladders

Yusuf

Yang

2002

Phys. Rev. B

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We study antiferromagnetic two-leg spin-1/2 ladders with strong bond randomness, using the real-space renormalization-group method. We find the low-temperature spin susceptibility of the system follows nonuniversal power laws, and that the ground-state spin-spin correlation is short ranged. Our results suggest that there is no phase transition when the bond randomness increases from zero; for strong enough randomness the system is in a Griffith region with divergent spin susceptibility and short-range spin-spin correlation.

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Section: Summary and Discussionmentioning

confidence: 99%

Thermodynamics of strongly disordered spin ladders

Yusuf

Yang

2002

Phys. Rev. B

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“…There are random quantum systems in which z depends on the initial disorder and z is approximately proportional to 1/α. This can be found, among others for random Heisenberg spin ladders [8]. In other systems with frustration, z is disorder independent (see the three-dimensional spin glass models [10]), and large spins are formed in these cases, as discussed in the following section.…”

Section: Strong Disorder Fixed Pointmentioning

confidence: 83%

“…There is singlet formation if S 1 = S 2 are coupled antiferromagnetically, in which case the pair of spin S 1 and S 2 is eliminated and the renormalized couplings are calculated by second order perturbation theory. The expression of the renormalized couplings can be found in the literature [7,8,10,14].…”

Section: Heisenberg Modelmentioning

confidence: 99%

“…The renormalization rules, as given in the literature [7,8,10,14] involve two processes: spincluster formation and singlet formation. Two spins S 1 and S 2 coupled by a strong exchange |J 1,2 | ∼ Ω give rise to a spin S = S 1 +S 2 if J 1,2 < 0 (ferromagnetic coupling) and to a spin S = |S 1 − S 2 | if J 1,2 > 0 (antiferromagnetic coupling) and S 1 = S 2 .…”

Section: Heisenberg Modelmentioning

confidence: 99%

“…Infinite disorder fixed points can be found in several 1D systems, for instance in the random transverse field Ising chain [3], random antiferromagnetic Heisenberg chain [4], tight-binding model, equivalent in 1D to the random XX model by a Jordan-Wigner transformation. Strong disorder fixed points are characterized by Griffiths phases [5,6] in the Heisenberg chain with randomly mixed ferro-and antiferromagnetic couplings [7] and in random quantum ladders [8].…”

Section: Introductionmentioning

confidence: 99%

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We use a numerical implementation of the strong disorder renormalization group (RG) method to study the low-energy fixed points of random Heisenberg and tight-binding models on different types of fractal lattices. For the Heisenberg model new types of infinite disorder and strong disorder fixed points are found. For the tight-binding model we add an orbital magnetic field and use both diagonal and off-diagonal disorder. For this model besides the gap spectra we study also the fraction of frozen sites, the correlation function, the persistent current and the two-terminal current. The lattices with an even number of sites around each elementary plaquette show a dominant φ0 = h/e periodicity. The lattices with an odd number of sites around each elementary plaquette show a dominant φ0/2 periodicity at vanishing diagonal disorder, with a positive weak localization-like magnetoconductance at infinite disorder fixed points. The magnetoconductance with both diagonal and off-diagonal disorder depends on the symmetry of the distribution of on-site energies.

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Density Matrix Renormalization

Hallberg¹

Theoretical Methods for Strongly Correlated Electrons

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The Density Matrix Renormalization Group (DMRG) has become a powerful numerical method that can be applied to low-dimensional strongly correlated fermionic and bosonic systems. It allows for a very precise calculation of static, dynamical, and thermodynamical properties. Its field of applicability has now extended beyond Condensed Matter, and is successfully used in statistical mechanics and high-energy physics as well. In this chapter, we briefly review the main aspects of the method. We also comment on some of the most relevant applications so as to give an overview on the scope and possibilities of DMRG and mention the most important extensions of the method, such as the calculation of dynamical properties, the application to classical systems; inclusion of temperature, phonons and disorder, field theory; time-dependent properties, and the ab initio calculation of electronic states in molecules.

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Strongly disordered spin ladders

Cited by 56 publications

References 55 publications

Thermodynamics of strongly disordered spin ladders

Thermodynamics of strongly disordered spin ladders

Strong-disorder renormalization-group method on fractal lattices: Heisenberg models and magnetoresistive effects in tight-binding models

Density Matrix Renormalization

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